1.

the digits of a two digit number differ by 3.If the digits are interchanged and added to the original number the number obtained is 143. Find both the numbers.(use only one variable)

Answer»

The answer is given below :

Since, the difference between the digits of the NUMBER is 3, we consider the numbers as (x + 3) and x at tens and ones place respectively.
where (x + 3) - x = 3.

Then, the number is

= 10(x + 3) + x

= 10x + 30 + x

= (11x + 30)

When the digits are interchanged, the number is

= 10x + (x + 3)

= (11x + 3)

By the given condition,

ORIGINAL number + New number = 143

⇒ (11x + 30) + (11x + 3) = 143

⇒ 22X + 33 = 143

⇒ 22x = 143 - 33

⇒ 22x = 110

⇒ x = 110/22

⇒ x = 5

So, the digit at ones place is 5 and the digit is tens place is (5 + 3) = 8.

So, the numbers are 85 and 58.

Thank you for your question.


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